Reachability and asymptotics of Gaussian Transformer dynamics

In three linesTheoretical study formalizes data propagation through Transformers as a nonlinear control system. For mean-field Transformer with self-attention and affine feed-forward layers, Gaussian distributions remain exactly Gaussian. This reduces dynamics to finite-dimensional bilinear control system governing mean and covariance evolution, connecting Transformer expressivity to Riccati-type equations.

Summary generated by Claude — human-verified